The development of efficient and rapid technologies for the optical tracking of individual molecules or particles makes it possible to investigate dynamic biological processes or the rheological behaviour of complex fluids, such as polymer networks, often in a non-invasive manner. Interest is generally directed at the ability to create well focused images of an object in a 3D volume.
In most cases, the nanometric object is a fluorescent emitter, whose signal is collected using a “wide-field” detection system, in which the entire field of view of a microscope is illuminated with simultaneous detection of the fluorescence emitted using a camera. Superposing multiple frames detected in sequence and using appropriate interpolation procedures, it is possible to obtain the two-dimensional localisation of the emitter.
The typical resolution of a microscope in visible light causes nanometric objects spread out in a sample appear in the image as luminous diffraction spots. The impulsive response of an optical instrument is commonly defined by the Point Spread Function (PSF), i.e. the amplitude distribution of the electromagnetic field on the image plane when a point source is observed. In the case of a non-point source, for example in the case of particles of at least a few tens of nm, the apparent dimension of the particle substantially corresponds to the dimension of the luminous spot and it is the convolution of the real dimension with the PSF.
Two main questions have been addressed in the development of techniques for the localisation of a single emitter in a volume instead of in a plane, i.e. the 3D localisation.
The first question pertains to the loss of efficiency of photonic collection from objects positioned outside the focal plane. In this case, single emitters do not appear as spots but as diffraction rings. The diffusion of light in rings with the consequent loss of the measured intensity results in decreased precision in the 2D localisation outside the focal plane until reaching an inability to localise the emitter. A second point resides in the fact the axial symmetry along the z-axis of the PSF in common microscopes does not allow discriminating whether an object is positioned at a distance Δz above or below the focal plane.
In other words, the axial distance traveled by a particle in a plane (x,y) can be determined by measuring the diameter of the first diffraction ring (if the dimension of the particle is known), however, it is not possible to determine, along the z-axis, whether the particle moved above or below the focal plane.
Moreover, the reduction of the signal/noise ratio when the particle moves out of focus limits in fact the axial distance within which the particle is visible.
A system for 3D tracking of a single fluorescent molecule, called Parallax, was presented in “Parallax: High Accuracy Three-Dimensional Single Molecule Tracking Using Split Images” di Y. Sun et al., Nano Letters, vol. 9, pages 2676-2682 (2009). The light beam emitted by an object is collimated by a lens positioned at a focal length to the primary image and separated in two optical paths by mirrors positioned at an additional focal length. The two optical paths form two images on the upper and lower part of the camera separated by a distance Δy1. When the object if out of focus, the beam is no longer collimated and the separate images formed on the camera are closer or farther away to or from each other in the y direction, with separation Δy2. The separation between Δy1 and Δy2 provides the signal to measure the displacement of the object along the z axis, while the positions in the plane (x,y) are obtained by the average of the positions in the two images.
The application US 2014/0192166 describes a microscope for generating a 3D image of an object that comprises a first and a second detector, an optical system that includes a waveplate between the 3D object and the detectors, wherein the waveplate is configured in such a way that the optical system simultaneously produces a depth of field extended to the second detector and the depth-encoded image exhibits a PSF that maps the positioning in various points inside the 3D object.
Use of a lens with variable/tunable focal length, often indicated with a varifocal lens, in a microscope, when positioned in a conjugated plane of the rear focal plane of the microscope lens, makes it possible to obtain focused images on the focal planes selectable by a user. If the speed of displacement of the focal spot of a varifocal lens is greater than the exposure time of the detector, the information on multiple plane can be integrated in a single image capture, creating an extended depth of field (EDOF) effect.
Sheng Liu and Hong Hua in “Extended depth-of-field microscopic imaging with a variable focus microscope objective”, published in Optics Express, vol. 19, pages 353-362 (2011), have a microscope able to capture EDOF images in a single captured image. The volumetric optical sampling method uses a rapid scan of the focus of a varifocal objective lens through the extended depth of a thick sample during a single exposure of a detector. The captured image is the fusion of infinite sections (slices) of image within the focal interval of the objective lens and an EDOF image is reconstructed by applying the deconvolution technique. In the optical system used, a miniature liquid lens is attached to the rear surface of the objective. The simultaneous imaging of multiple focal planes was applied in “wide-field” microscopes to extend the axial tracking of a nanometric emitter.
M. Duocastella et al. in “Three-dimensional particle tracking via tunable color-encoded multiplexing”, published in Optics Letters Vol. 41, Issue 5, pp. 863-866 (2016), describe a method for 3D tracking in light field optical microscopy using multiple, selectable focal planes. A lens with electronically tunable focal length and high speed is synchronised with three different sources of monochromatic light, each with different colour, red, white and blue (RGB). The control electronics makes possible the selection and independent control of the position whereat each colour is focused. In this way, each individual exposure by means of a colour camera simultaneously captures the three colours corresponding to the three different focal planes. The authors observe that measuring the diameter and the position of the centroid of the diffraction rings for each of the three focal planes allows the localisation and tracking of individual objects in significantly larger axial intervals than those obtainable with conventional approaches with single focal plane.
S. Ram et al. “High Accuracy 3D Quantum Dot Tracking with Multifocal Plane Microscopy for the Study of Fast Intracellular Dynamics in Live Cells”, published in Biophys J. (2008); vol. 95(12), pages 6025-6043, describe a localisation algorithm for determining the 3D position of a point source in a multifocal plane microscopy image mode, in which the simultaneous imaging of two distinct planes within the sample is generated.